Menu

Book Report: Scale

“Even though the conceptual and mathematical structure of the growth equation is the same for organisms, social insect communities, and cities, the consequences are quite different: sublinear scaling and economies of scale that dominate biology lead to stable bounded growth and the slowing down of the pace of life, whereas superlinear scaling and increasing returns to scale that dominate socioeconomic activity lead to unbounded growth and to an accelerating pace of life.” (Scale)

Origin:Issue 050 of Nautilus included an article, Why New York is Just an Average City, which examined the scaling laws that govern the growth of cities. That article was an adaptation of some of the subject matter of Scale, which is how I became aware of the book.

Why did I buy and read Scale? I guess partly because I have a general interest in the mathematical laws that explain the world in which we live, and partly because I thought West’s examinations of cities and of companies, in particular, might have some applications or usefulness in my professional life.

But perhaps more-so, because the subject just seemed neat: universal laws that apply to biological systems, cities, economies, and companies? Cool!

Summary:Scale is both a story about the remarkable career of Geoffrey West and an exposition of hidden scaling forces that shape our world and have profound (and somewhat unpleasant) ramifications for our future.

The opening chapter, The Big Picture, serves as a summary for the remainder of the book: it introduces the main concepts, explains the implications and ramifications, and teases the with conclusions that will be covered in detail in the remainder of the book.

From there, West gives readers a crash-course in scaling (The Measure of All Things – An Introduction to Scaling), as these concepts will be important for understanding the properties covered in later chapters. The math isn’t too complicated, and the main points are clearly made, so readers lacking a strong mathematical background can still appreciate what’s to come.

The next two chapters (The Simplicity, Unity, and Complexity of Life and The Fourth Dimension of Life – Growing, Aging and Death) examine scaling in the biological world, and explains the physical origins of quarter power mathematical scaling laws that arise in many biological systems as a result of three extraordinarily simple network characteristics. Simply put, these chapters will blow your mind.

Demonstrating the universality of scaling laws, the subject matter transitions to examining cities as complex systems with emergent characteristics. The next four chapters (From the Anthropocene to the Urbanocene – A Planet Dominated by Cities, A Prelude to A Science of Cities, Toward a Science of Cities, and Consequences and Predictions – From Mobility and the Pace of Life to Social Connectivity, Diversity, Metabolism, and Growth) demonstrate how the emergent behaviour of cities has surprising similarity and also important differences when compared to biological systems, with network effects still serving as the foundation.

At this point, West explores the early research into scaling effects on companies (Toward a Science of Companies), which seem to display their own version of self-similarity and scaling that is subtly different from both biological systems and cities.

West closes off Scale with a call to action, imploring the world to take a multi-system approach that examines sustainability by considering the realities and ramifications of scaling effects.

My Take: Let me start with a personal anecdote. A couple of years ago, I was lying in bed finishing up a book. Upon completing it, I closed it with a satisfied thwap, walked to my ‘library’, replaced the book on a shelf, grabbed another, jumped back into bed, and cracked open this new tome. At this point, my wife remarked, “You’re starting another? What are you going to do with all this knowledge?” I didn’t really have an answer then, nor do I now.

I was reminded of this exchange while reading Scale. More than most books I’ve read, the information within is both esoteric and of little practical value to my day-to-day. Don’t get me wrong: the content is fascinating and the conclusions have enormous ramifications for the socioeconomic stability of human civilizations, but I don’t see how my behaviour is going to change.

That’s not to suggest that I didn’t enjoy Scale, although there were definitely times when I really wanted to be done (it’s looong): I’m definitely grateful that I’m now better aware of scaling issues and concepts (I think those might have practical value at some point in my life or career), and I’m certainly struck by the beauty and order that’s hidden in this complex world of ours. I also learned about a long list of interesting people, and came across some ‘old friends’ who have a habit of popping up in my reading material.

It’s just that Scale is quite academic, extremely thorough, and deals with subject matter so abstract (albeit with very real physical manifestations) that I struggle to see how I can actually, y’know, do something with the knowledge.

Read This Book If: …You’re a nerd; or, I suppose, if you’re some sort of policymaker who deals with economies, cities, or sustainability of human civilization.

Notes and Quotes

The Big Picture

“A typical complex system is composed of myriad individual constituents or agents that once aggregated take on collective characteristics that are usually not manifested in, nor could easily be predicted from, the properties of the individual components themselves.“

p11, reminded me of my trips to Rotterdam, which was essentially flattened in World War 2: “Cities are remarkably resilient and the vast majority persist. Just think of the awful experiment that was done seventy years ago when atom bombs were dropped on two cities, yet just thirty years later they were thriving.”

p17 and 18 make an important point about normalizing data, backed up with various data points, and demonstrated/examined in detail in later chapters: “Simple linear proportionality, implicit in using per capita measures, is almost never valid. GDP, like almost any other quantifiable characteristic of a city, or indeed of almost any complex system, typically scales nonlinearly.”

p21, unsurprisingly reminiscent of Emergence: “A typical complex system is composed of myriad individual constituents or agents that once aggregated take on collective characteristics that are usually not manifested in, nor could easily be predicted from, the properties of the individual components themselves.”

p26 introduces Klieber’s Law, which I’ve come across in quite a few books and articles over the years…pretty amazing stuff

p31, summarizing the ramifications of scaling laws for cities, and the unfortunate likelihood of a finite time singularity (note that this phenomenon is different from a Malthusian collapse): “In a nutshell, the problem is that the theory also predicts that unbounded growth cannot be sustained without having either infinite resources or inducing major paradigm shifts that ‘reset’ the clock before potential collapse occurs.”

p31, with another serious catch…we can put off the finite time singularity with innovations, but, “Theory dictates that such discoveries must occur at an increasingly accelerating pace; the time between successive innovations must systematically and inextricably get shorter and shorter.”

p32, with the kicker: “This is clearly not sustainable, potentially leading to the collapse of the entire urbanized socioeconomic fabric.”

The Measure of All Things – An Introduction to Scaling

“Galileo asked what happens if you try to indefinitely scale up an animal, a tree, or a building, and with his response discovered that there are limits to growth. His argument set the basic template for all subsequent scaling arguments right up to the present day.“

The first few pages of this chapter talk about Galileo’s insights about scaling, explained in Discourses and Mathematical Demonstrations Relating to Two New Sciences…and man, it really is pretty amazing what the guy figured out back in the day: “Galileo asked what happens if you try to indefinitely scale up an animal, a tree, or a building, and with his response discovered that there are limits to growth. His argument set the basic template for all subsequent scaling arguments right up to the present day.”

p54, with something I’d never considered, but which is of crucial importance in pharmacology (but which seems not to be appreciated, if one looks at dosing guidelines): “Drugs, like metabolites and oxygen, are typically transported across surface membranes, sometimes via diffusion and sometimes through network systems. As a result, the dose-determining factor is to a significant degree constrained by the scaling of surface areas rather than the total volume or weight of an organism, and these scale nonlinearly with weight.”

p63 introduced me to, “an extraordinary man with an extraordinary name: Isambard Kingdom Brunel… Many consider him the greatest engineer of the nineteenth century, a man whose vision and innovations, particularly concerning transport, helped make Britain the most powerful and richest nation in the world.” Well OK then.

p69 covers a recurring theme in many of my books: that major advances are, in reality, achieved through the gradual accumulation of knowledge, by trial and error, by tinkering, by experimentation, etc.

p74, with a neat example of how many (most?) models should use non-linear scaling: “Let me give you a simple illustration of this by asking how fast a 10-foot-long model ship would have to move to mimic the motion of the 700-foot-long Great Eastern moving at 20 knots (a little over 20 mph). If they are to have the same Froude number (that is, the same value of the square of their velocity divided by their length), then the velocity must scale as the square root of their lengths… In other words, the dynamics of a 10-foot-long model ship moving at just 2.5 knots simulates that of the 700-foot-long Great Eastern moving at 20 knots.”

Man, it’s amazing how discoveries and research from ages ago are applicable today, p78: “Rayleigh‘s mathematical analysis of the scattering of waves formed the basis of what became known as ‘scattering theory.’ Its application to many problems, from water waves to electromagnetic waves and especially radar, and more recently IT communication, has been incredibly important, not least its role in the development of quantum mechanics. It provided the basis for the formalism developed for extracting discoveries from ‘scattering experiments’ performed at large particle accelerators such as CERN in Geneva, where the famous Higgs particle was recently discovered.”

The Simplicity, Unity, and Complexity of Life

“As a physicist, it seemed to me that these ‘universal’ quarter-power scaling laws were telling us something fundamental about the dynamics, structure, and organization of life. Their existence strongly suggested that generic underlying dynamical processes that transcend individual species were at work constraining evolution.“

p98: “As a physicist, it seemed to me that these ‘universal’ quarter-power scaling laws were telling us something fundamental about the dynamics, structure, and organization of life. Their existence strongly suggested that generic underlying dynamical processes that transcend individual species were at work constraining evolution. This therefore opened a possible window onto underlying emergent laws of biology and led to the conjecture that the generic coarse-grained behavior of living systems obeys quantifiable laws that capture their essential features.”

Wow, this is pretty cool, from p100: “Here’s something truly extraordinary that you should know about yourself: every day you typically make about 2 x 10^26 ATP molecules – that’s two hundred trillion trillion molecules – correspond to a mass of about 80 kilograms (about 175 lbs.). In other words, each day you produce and recycle the equivalent of your own body weight of ATP!”

p100…I feel like comparing this number to the one in I Contain Multitudes: “Your body is composed of about a hundred trillion (10^14) cells.”

p103: “As I began to ponder what the origins of these surprising scaling laws might be, it became clear that whatever was at play had to be independent of the evolved design of any specific type of organism, because the same laws are manifested by mammals, birds, plants, fish, crustacea, cells, and so on.”

“Functionally, biological systems are ultimately constrained by the rates at which energy, metabolites, and information can be supplied through these networks.”

p103, somewhat reminiscent of nations and warfare: “Functionally, biological systems are ultimately constrained by the rates at which energy, metabolites, and information can be supplied through these networks. Examples include animal circulatory, respiratory, renal, and neural systems, plant vascular systems, intracellular networks, and the systems that supply food, water, power, and information to human societies.”

I just really liked this description from p108, and I can’t help but think the world would be better off if other fields (e.g., politics) genuinely encouraged challenges, skepticism, testing, etc.: “To varying degrees, all theories and models are incomplete. They need to be continually tested and challenged by increasingly accurate experiments and observational data over wider and wider domains and the theory modified or extended accordingly. This is an essential ingredient in the scientific method. Indeed, understanding the boundaries of their applicability, the limits to their predictive power, and the ongoing search for exceptions, violations, and failures has provoked even deeper questions and challenges, stimulating the continued progress of science and the unfolding of new ideas, techniques, and concepts.”

p109, with some good advice when creating models: “The challenge at every level of observation is to abstract the important variables that determine the dominant behavior of the system.”

“The challenge at every level of observation is to abstract the important variables that determine the dominant behavior of the system.”

p112, on allometric scaling laws: “Formulating a set of general network principles and distilling out the essential features that transcend the huge diversity of biological networks proved to be a major challenge that took many months to resolve… Once the dust had settled, we proposed the following set of generic network properties that are presumed to have emerged as a result of the process of natural selection and which give rise to quarter-power scaling laws when translated into mathematics. In thinking about them, it might be useful to reflect on their possible analogs in cities, economies, companies, and corporations…” The three network properties are: space filling, the invariance of terminal units, and optimization. These deceptively simple properties are explained in detail and give rise to the quarter-power scaling laws that appear all over the place in biological systems.

p120, neato! “To avoid [the potential problem of wave reflection] and minimize the work our hearts have to do, the geometry of our circulatory systems has evolved so that there are no reflections at any branch point throughout the network. The mathematics and physics of how this is accomplished is a little bit complicated, but the result is simple and elegant: the theory predicts that there will be no reflections at any branch point if the sum of the cross-sectional areas of the daughter tubes leaving the branch point is the same as the cross-sectional area of the parent tube coming into it.”

p121, with a cool supporting graphic: “An interesting consequence of area-preserving branching is that the cross-sectional area of the trunk is the same as the sum of the cross-sectional areas of all the tiny branches at the end of the network (the petioles). Amazingly, this was known to Leonardo da Vinci.”

p122, on impedance matching (TIL): “The bones in the middle ear provide impedance matching between the eardrum and the inner ear. If you have ever witnessed or been subject to an ultrasound examination you will be familiar with the nurse or technician smearing a gooey gel over your skin before sliding the probe over it. You probably thought that this was for lubrication purposes but in fact it’s actually for matching impedances.”

p134 (again, just kind’ve neat): “Consequently, the frequency distribution of wars follows simple power law scaling indicating that conflicts are approximately self-similar. This remarkable result leads to the surprising conclusion that, in a coarse-grained sense, a large war is just a scaled up version of a small conflict, analogous to the way that elephants are approximately scaled-up mice.”

p141 had me thinking an idea that I’ve had time and again: that markets are fractal in nature, with each subdividing into a multitude of smaller sub-markets, and so on, in a self-similar fashion.

“Driven by the forces of natural selection to maximize exchange surfaces, biological networks do achieve maximal space-filling and consequently scale like three-dimensional volumes rather than two-dimensional Euclidean surfaces. This additional dimension, which arises from optimizing network performance, leads to organisms’ functioning as if they are operating in four dimensions. This is the geometric origin of the quarter power.“

I mean, how utterly cool is this??? p153: “Driven by the forces of natural selection to maximize exchange surfaces, biological networks do achieve maximal space-filling and consequently scale like three-dimensional volumes rather than two-dimensional Euclidean surfaces. This additional dimension, which arises from optimizing network performance, leads to organisms’ functioning as if they are operating in four dimensions. This is the geometric origin of the quarter power. Thus, instead of scaling with classic 1/3 exponents, as would be the case if they were smooth nonfractal Euclidean objects, they scale with 1/4 exponents. Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional.”

“Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional.”

p154: “This is testimony to the power of natural selection to have exploited variations on this fractal theme to produce an incredible variety of biological forms and functions. But it is also testimony to the severe geometric and physical constraints on metabolic processes which have dictated that all of these organisms obey a common set of quarter-power scaling laws. Fractal geometry has literally given life an added dimension.”

p166, on why growth stops: “So the rate at which energy is needed for maintenance increases faster than the rate at which metabolic energy can be supplied, forcing the amount of energy available for growth to systematically decrease and eventually go to zero, resulting in the cessation of growth. In other words, you stop growing because of the mismatch between the way maintenance and supply scale as size increases.” A few lines later, there’s this specific explanation: “The increase in the number of supply units (the capillaries) cannot keep up with the demands from the increase in the number of customers (the cells).”

p173: “The critical take-home message from this section is that sublinear scaling and the associated economies of scale arising from optimizing network performance lead to bounded growth and the systematic slowing of the pace of life. This is the dynamic that dominates biology.”

p177, on the impact of small temperature changes on metabolic rates: “A modest 2°C change in ambient temperature leads to a 20 percent to 30 percent change in growth and mortality rates. This is huge and therein lies our problem. If global warming induces a temperature increase of around 2°C, which it is on track to do, then the pace of almost all biological life across all scales will increase by a whopping 20 percent ot 30 percent.”

p183, with an interesting health policy proposal: “We have become obsessed with extending our life spans regardless of cost, whereas it may make greater sense to put the emphasis on maintaining and extending health span – that is, living a fuller life in an appropriately healthy body with a reasonably healthy mind and dying when these systems are clearly no longer functional.”

p186, with another parallel to Emergence: “The city as the engine for social change and increasing well-being is one of the truly great triumphs of our amazing ability to form social groups and collectively take advantage of economies of scale.”

From the Anthropocene to the Urbanocene – A Planet Dominated by Cities

“From a scientific perspective the truly revolutionary character of the Industrial Revolution was the dramatic change from an open system where energy is supplied externally by the sun to a closed system where energy is supplied internally by fossil fuel. This is a fundamental systemic change with huge thermodynamic consequences.“

p221 has a great example that uses a bacteria colony to illustrate the risks associated with exponential growth and constrained resources

p229, with a great quote from Kenneth Boulding: “anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist.”

p233 talks a bit about the risks of unregulated corporate and political ambition

p233: “Independent of how superbly innovative we are, ultimately everything is driven and processed by the use of energy, and the processing of energy has inevitable deleterious consequences.”

p235, making the point that urbanization and increases in energy demands could create an effective population demand of more than a trillion people, even if the world’s population is only at 10 billion

p236: “From a scientific perspective the truly revolutionary character of the Industrial Revolution was the dramatic change from an open system where energy is supplied externally by the sun to a closed system where energy is supplied internally by fossil fuel. This is a fundamental systemic change with huge thermodynamic consequences, because in a closed system the Second Law of Thermodynamics and its requirement that entropy always increases strictly applies. We ‘progressed’ from an external, reliable, and constant source of energy to one that is internal, unreliable, and variable. Furthermore, because our dominant source of energy is now an integral component of the very system it is supporting, its supply is hostage to continually internal market forces.”

p240: “Consequently, the long-term strategy for sustained global energy availability is clear: we need to return to the biological paradigm where most of our energy needs are supplied directly from the sun but in such a way as to maintain and expand what we have so far accomplished… One of the more mysterious aspects of the twenty-first century is that those who seem most vocal in promoting and celebrating innovation and the free market economy as the engine of sustainability seem so reluctant to recognize the urgency of the challenge and to champion research and development in exploiting the almost infinite power of solar energy.”

A Prelude to A Science of Cities

“Macroeconomically, cities are the prime drivers of economic development, not the nation-state as is typically presumed by most classical economists.“

p252 has me thinking about what the term ‘smart cities’ really should mean: “In fact, the real essence of a city is its people – they provide its buzz, its soul, and its spirit, those indefinable characteristics that we viscerally feel when we are participating in the life of a successful city. This may seem obvious, but the emphasis of those who think about cities, such as planners, architects, economists, politicians, and policy makers, is primarily focused on their physicality rather than on the people who inhabit them and how they interact with one another. It is all too often forgotten that the whole point of a city is to bring people together, to facilitate interaction, and thereby to create ideas and wealth, to enhance innovative thinking and encourage entrepreneurship and cultural activity by taking advantage of the extraordinary opportunities that the diversity of a great city provides.”

Here’s a classic Jacobs quote, which I think is applicable well beyond city planning: “The pseudoscience of planning seems almost neurotic in its determination to imitate empiric failure and ignore empiric success.”

p262, of Jacobs: “A major point throughout her writing is that macroeconomically, cities are the prime drivers of economic development, not the nation-state as is typically presumed by most classical economists. This was a radical idea at the time and almost entirely ignored by economists, especially as Jane was not a card-carrying member of the clan. Obviously the economy of a country is strongly interrelated with the economic activity of its cities, but, like any complex adaptive system, the whole is greater than the sum of its parts. Almost fifty years after Jane’s hypotheses about the primacy of cities in national economies were articulated, many of us who have come to study cities from a variety of perspectives have arrived at some version of her conclusions. We live in the age of the Urbanocene, and globally the fate of the cities is the fate of the planet.”

p264 talks about Hollerith punch cards as generating a “nightmarish nostalgia” for West…I wonder what my version will be?

p266 talks about soullessness and alienating nature of planned cities, and it reminds me of the early (I hope we don’t keep making the same mistakes) attempts at planned forests (e.g., reclaimed industrial land)…rows of trees, devoid of shrubs, insects, larger animals, etc. Gotta just let things emerge. Actually, on that note, Nautilus also had a neat feature related to this idea: Reinventing Staten Island.

Toward a Science of Cities

“In marked contrast to infrastructure, which scales sublinearly with population size, socioeconomic quantities – the very essence of a city – scale superlinearly, thereby manifesting systematic increasing returns to scale.“

p275, of cities: “The greater efficiency that comes with size has the nonintuitive but very important consequence that on average the bigger the city, the greener it is and the smaller its per capita carbon footprint. In this sense, New York is the greenest city in the United States.”

p275: “These metrics not only scale in an extremely simple fashion following classic power law behavior, but they all do it in approximately the same way with a similar exponent of approximately 1.15 regardless of the urban system. So in marked contrast to infrastructure, which scales sublinearly with population size, socioeconomic quantities – the very essence of a city – scale superlinearly, thereby manifesting systematic increasing returns to scale. The larger the city, the higher the wages, the greater the GDP, the more crime, the more cases of AIDS and flue, the more restaurants, the more patents produce, and so on, all following the ’15 percent rule’ on a per capita basis in urban systems across the globe.”

p278 (they really are!): “These results are pretty amazing. We typically think of each city, and especially the one we live in, as being unique, with its own history, geography, and culture, having its own special individuality and character that we feel we recognize. Boston not only looks different but also ‘feels’ different from New York, San Francisco, or Cleveland, just as Munich looks and feels different from Berlin, Frankfurt, or Aachen. And they do and are. But who would believe that within their own urban systems they are approximately scaled versions of one another, at least as far as almost anything that you can measure about them is concerned? If you are given the size of a city in the United States, for example, then you can predict with 80 to 90 percent accuracy what the average wage is, how many patents it’s produced, how long all of its roads are, how many AIDS it’s had, how many lawyers and doctors it has, et cetera.”

p279, continuing the general thought: “The data convincingly show that despite appearances cities are approximately scaled versions of one another… These extraordinary regularities open a window onto underlying mechanisms, dynamics, and structures common to all cities and strongly suggest that these phenomena are in fact highly correlated and interconnected, driven by the same underlying dynamics and constrained by the same set of ‘universal’ principles.”

A footnote on p300 mentions Steve Strogatz‘ book The Joy of X, which sounds interesting (to me)

p302, on why good people do bad things, after a section summarizing some results from the experiments of Stanley Milgram and Philip Zimbardo: “Zimbardo has become an articulate and vocal advocate for the recognition that this powerful dynamic, which seems to be built into our psyches independent of cultural origins and which has wreaked horrors over the centuries, be explicitly recognized and addressed rather than resorting to our instinctual tendency to put the blame simplistically on individual ‘bad apples,’ national characteristics, or cultural norms.”

p310 talks a bit about Zipf’s law, which has popped up in several books I’ve read

Consequences and Predictions – From Mobility and the Pace of Life to Social Connectivity, Diversity, Metabolism, and Growth

“In other words, [a per capita indicator] presumes that an idealized city is just the linear sum of the activities of all of its citizens, thereby ignoring its most essential feature and the very point of its existence, namely, that it is a collective emergent agglomeration resulting from nonlinear social and organizational interactions.“

p330 (long-time readers know that I have a thing for geography, maps, and historical context…this passage refers to An Atlas of Economic Geography, created in 1914 by John Bartholomew): “One of his unique illustrations was a world map showing how long it took to get to any general area on the planet. It’s quite illuminating. For instance, the boundaries of Europe were about five days’ journey apart, whereas today they have shrunk to a mere few hours. Similarly, the boundaries of the British Empire extended over several weeks in 1914, but today its ghostly remains can be traversed in less than a day. Most of central Africa, South America, and Australia required in excess of forty days’ travel, and even Sidney was over a month away.”

p331…I’m struck that all past economist and futurist predictions about shorter workweeks and crazy amounts of leisure time presumed that absolute demand for work/output would stay constant, and that there wouldn’t be a relentless desire for more…which seems laughably ignorant

This conclusion from p333, summarizing findings of Yacov Zahavi, is deceptively profound: “So the increase in transportation speed resulting from the marvelous innovations of the past couple of hundred years has been used to increase commuting distances. People have taken advantage of these advancements to live farther away and simply travel longer distances to work. The conclusion is clear: the size of cities has to some degree been determined by the efficiency of their transportation systems for delivering people to their workplaces in not much more than half an hour’s time.”

p355: “In other words, [a per capita indicator] presumes that an idealized city is just the linear sum of the activities of all of its citizens, thereby ignoring its most essential feature and the very point of its existence, namely, that it is a collective emergent agglomeration resulting from nonlinear social and organizational interactions.”

p374: “Even though the conceptual and mathematical structure of the growth equation is the same for organisms, social insect communities, and cities, the consequences are quite different: sublinear scaling and economies of scale that dominate biology lead to stable bounded growth and the slowing down of the pace of life, whereas superlinear scaling and increasing returns to scale that dominate socioeconomic activity lead to unbounded growth and to an accelerating pace of life.”

Toward a Science of Companies

“A crucial aspect of the scaling of companies is that many of their key metrics scale sublinearly like organisms rather than superlinearly like cities. This suggests that companies are more like organisms than cities and are dominated by a version of economies of scale rather than by increasing returns and innovation.“

p391: “A crucial aspect of the scaling of companies is that many of their key metrics scale sublinearly like organisms rather than superlinearly like cities. This suggests that companies are more like organisms than cities and are dominated by a version of economies of scale rather than by increasing returns and innovation. This has profound implications for their life history and in particular for their growth and mortality.”

p392: “The nonlinear scaling of maintenance expenses in younger companies, buoyed by investments and the ability to borrow large amounts relative to their size, fuels their rapid growth. Consequently, the idealized growth curve of companies has characteristics in common with classic sigmoidal growth in biology in that it starts out relatively rapidly but slows down as companies become larger and maintenance expenses transition to becoming linear. However, unlike biology, whose maintenance costs do not transition to linearity, companies do not cease growing but continue to grow exponentially, though at a more modest rate.”

p393: “As can be clearly seen in Figure 70 where the overall market growth has been factored out, all large mature companies have stopped growing. Their growth curves when corrected for both inflation and the expansion of the market now look just like typical sigmoidal growth curves of organisms in which growth ceases at maturity.”

p397, very counterintuitively: “The general dynamics and overall life history of companies are effectively independent of the business sector in which they operate. This strongly suggests that there is indeed a universal dynamic at play that determines their coarse-grained behavior, independent of their commercial activity or whether they are eventually going to go bankrupt or merge with or be bought by another company. In a word, this strongly supports the idea of a quantitative science of companies. This is really quite amazing.”

The Vision of A Grand Unified Theory of Sustainability

“Because of the presence of a finite time singularity resulting from superlinear scaling, this scenario is categorically different from that of Malthus.“

p412, a call to action: “We need a broad and more integrated scientific framework that encompasses a quantitative, predictive, mechanistic theory for understanding the relationship between human-engineered systems, both social and physical, and the ‘natural’ environment – a framework I call a grand unified theory of sustainability. It’s time to initiate a massive international Manhattan-style project or Apollo-style program dedicated to addressing global sustainability in an integrated, systemic sense.”

p414 expands on the inconvenient problem of a finite time singularity, and distinguishes it from a Malthusian collapse: “Because of the presence of a finite time singularity resulting from superlinear scaling, this scenario is categorically different from that of Malthus. If growth were purely exponential as assumed by Malthusians, neo-Malthusians, their followers, and critics, then the production of energy, resources, and food could at least in principle keep up with exponential expansion because all of the relevant characteristics of the economy or city remain finite, even if they continue to increase in size and become very large. This cannot be achieved if you are growing superexponentially and approaching a finite time singularity. In this scenario demand gets progressively larger and larger, eventually becoming infinite within a finite period of time.”

Afterword

This section basically just talks about the Sante Fe Institute, which really does sound like an interesting place that should be emulated in many locations worldwide

Postscript and Acknowledgments

Haha, loved this part from p454: “I am particularly grateful to Cormac [McCarthy] for painstakingly reading and editing the manuscript in excruciating detail, providing extensive feedback, which helped greatly in improving the final product. Although I accepted most of his advice about grammar and sentence construction, I continue to argue with him over his total aversion to semicolons and exclamation marks; and his insistence on the Oxford comma.”